To produce plastic, Milan Company must order a raw material. The demand for the plastic is forecasted to be normally distributed with a mean of 185 gallons and a standard deviation of 115 gallons. Milan sells the plastic for EUR 20 per gallon. Milan purchases raw material for EUR 8 per gallon and Milan must spend EUR 3 per gallon to dispose of unused raw material due to government regulations. (One gallon of raw material yields one gallon of plastic.) If demand is more than Milan can make, then Milan sells only what they made, and the rest of demand is lost.

a) Suppose Milan purchases 150 gallons of raw material. What is the probability that they will run out of raw material

b) Suppose Milan purchases 250 gallons of raw material. How many gallons of demand on average would remain unfulfilled

c) Suppose Milan purchases 350 gallons of raw material. How much should they expect to spend on disposal costs

d) Suppose Milan wants to ensure that there is a 92% probability that they will be able to satisfy the customer's entire demand. How many gallons of raw material should they purchase?

e) How many gallons should Milan purchase to maximize its expected profit?